Ethiopian Calendar & Bahire Hasab (衣索比亞曆)

The Sea of Computation — Thirteen Months of Sunshine and the Computus That Fixes Fasika

Overview

Ethiopia keeps its own time. The Ge'ez calendar runs twelve months of exactly thirty days plus Pagumen — the famous 'thirteenth month' of five or six days — and stands seven to eight years behind the Gregorian count, so that September 2025 opened the Ethiopian year 2018. Layered on top is the Bahire Hasab, the 'Sea of Computation': the arithmetic the Ethiopian Orthodox Tewahedo Church has used since antiquity to fix every movable fast and feast of the year, from the three-day Fast of Nineveh through Great Lent to Fasika (Easter) and Pentecost. askTIAN serves both layers: any Gregorian date converted to its Ge'ez date, and any Ethiopian year unfolded into its complete liturgical skeleton — epact and metqi, the trumpet-day of Beale Metqi, the tewsak addition, and all eleven movable observances with both calendars' dates. The entire chain is proven against an independent algorithm: Fasika computed the church's traditional way must equal the Alexandrian Easter from Meeus's formula, and the tests assert exactly that for two hundred consecutive years.

Origin & history

The calendar is the Coptic-Alexandrian system inherited from Ptolemaic Egypt — twelve uniform months plus epagomenal days, with a leap day every four years and no century exception — carried into the Ethiopian highlands with Christianity in the fourth century and kept ever since with its own month names and its own era, the Amete Mihret ('Year of Mercy'), which counts from a fifth-century-computed Annunciation 5500 years after Creation. The Bahire Hasab descends from the Alexandrian computus defended at Nicaea: a nineteen-year lunar cycle (the wenber, 'chair'), an epact (abakte), and the metqi number that proclaims the paschal new moon. Ethiopian tradition credits its systematization to scholars in the line of Demetrius of Alexandria and calls the discipline by the name of the medieval handbook Abushakir.

The system never lapsed: Ethiopia's civil life still runs on the Ge'ez year — Enkutatash, the new year, is a national holiday on September 11 — and the Church still derives its fasts from the Bahire Hasab rather than from any imported table. Because the computus is pure arithmetic, it can be checked rather than trusted: this implementation's rules were double-sourced from Ethiopian Orthodox teaching materials and an independent reference implementation, and then the strongest possible verification was applied — the traditional chain (wenber → abakte/metqi → Beale Metqi → tewsak → Nineveh → +69 days) must reproduce the Alexandrian Easter computed by Meeus's completely unrelated algorithm, year after year for two centuries, alongside the published Fasika dates of 2024–2027. One delightful property the tests also prove: the tewsak table cannot miss — from every possible weekday of the Beale Metqi, the prescribed addition lands the Fast of Nineveh on a Monday.

How it works

Give the engine a Gregorian date or an Ethiopian year. A date is converted through the Julian Day Number against the Amete Mihret epoch (1 Meskerem 1 = JDN 1,724,221) — an epoch that reproduces reality unaided, placing Enkutatash 2018 on 2025-09-11 and the post-leap 2016 on 2023-09-12. The year is then unfolded: Amete Alem (the year plus 5500), the evangelist of the year (Matthew, Mark, Luke or John by remainder mod 4 — the six-day Pagumen falls only in a Year of Luke, asserted), then the computus: medeb = Amete Alem mod 19, wenber, abakte = 11×wenber mod 30, metqi = 19×wenber mod 30 with zero read as thirty. Metqi of fifteen or more places the Beale Metqi in Meskerem, thirteen or less in Tikimt — and the values one and fourteen are arithmetically impossible, a theorem the tests prove, so the rule has no gap. The weekday of the Beale Metqi selects the tewsak; adding it plus 120 days gives the Monday of Nineveh; every movable feast follows at its fixed offset. Everything returns in both calendars with weekdays. Pure compute, no LLM.

Good for

• Gregorian ↔ Ethiopian date conversion, correct across every leap boundary including 6 Pagumen itself
• The complete movable-feast calendar for any Ethiopian year — Nineveh, Lent, Hosanna, Siklet, Fasika, Erget, Pentecost
• Fixed feasts with true Gregorian dates: Enkutatash, Meskel, Genna (Ethiopian Christmas), Timket, Filseta
• The Bahire Hasab numbers themselves — wenber, abakte, metqi, tewsak — for liturgical or educational display
• The evangelist of the year and the leap/Pagumen structure for any year, past or future
• Serving Ethiopia's 120+ million people and its global diaspora their own calendar, verified rather than approximated
• Cross-checking any third-party Ethiopian date table against a monument-grade computus

Use cases

The Diaspora Calendar App

One call per year renders the full Ethiopian liturgical year — every fast and feast in both calendars with weekdays — for the communities in Washington, London and Tel Aviv who live on two calendars at once.

The Date Converter That Never Drifts

Birth certificates, land records and visas from Ethiopia carry Ge'ez dates; the JDN-based conversion handles any date since 1 AM, including the thirteenth month, with round-trips proven in tests.

The Fasting Companion

Surface today's position in the fasting year — inside Great Lent? Apostles' Fast begun? — by comparing the converted date against the year's computed observances.

The Enkutatash Countdown

New year on September 11 or 12? The epoch arithmetic answers automatically for any year — no lookup table, no 2099 cliff.

Key terms

Bahire Hasab

'Sea of Computation' — the Ethiopian Orthodox computus fixing all movable fasts and feasts; also called Abushakir after the medieval handbook.

Amete Alem / Amete Mihret

The Era of the World (year + 5500) and the Era of Mercy (the civil year) — the two counts every computation opens with.

Wenber

'Chair' — the year's seat in the nineteen-year lunar cycle: (Amete Alem mod 19) − 1, with 0 read as 18.

Abakte & Metqi

The epact (11×wenber mod 30) and its complement (19×wenber mod 30) — provably summing to a multiple of thirty, the theorem the tests assert.

Beale Metqi

The proclamation day of the paschal new moon: day metqi of Meskerem when metqi ≥ 15, of Tikimt when ≤ 13 — values 1 and 14 being arithmetically impossible.

Tewsak

The weekday-keyed addition {Sun 7, Mon 6, Tue 5, Wed 4, Thu 3, Fri 2, Sat 8} that lands Nineveh on a Monday from any starting weekday — a self-proving table.

Pagumen

The thirteenth month: five days, six in the leap year that always belongs to Luke — the year before a Year of John.

Enkutatash

Ethiopian New Year, 1 Meskerem — September 11 Gregorian, or September 12 following an Ethiopian leap year.

API

The askTIAN Ethiopian Calendar API serves the Ge'ez calendar and the full Bahire Hasab from pure arithmetic: JDN conversion against the Amete Mihret epoch (reproducing Enkutatash 2025-09-11 and the leap-shifted 2023-09-12 unaided), the complete computus chain with its internal theorems asserted at runtime (abakte+metqi ≡ 0 mod 30; metqi never 1 or 14; Nineveh always a Monday), all eleven movable feasts and seven fixed feasts in both calendars — and the whole chain proven equal to Meeus's independent Julian-Easter algorithm for 200 consecutive years, plus the published Fasika anchors 2024–2027. Pure compute, no LLM, 2 TIAN.

Endpoint: POST /trpc/ethiopianCalendar.year — 2 TIAN Points. See the API documentation and Playground.